Question

If a conical wire is stretched by two forces F applied, parallel to its length and In opposite direction. NoramI to end faces. The length of wire is L and its end radius are $r_1$ and $r_2$ Find out the extention produced (Given: Y=Young's modulus of wire)

• A. $\frac{FL}{\pi r^2_1 Y}$
• B. $\frac{FL}{\pi r_1 Y}$
• C. $\frac{FL}{\pi r_1r_2 Y}$
• D. $\frac{FL}{\pi r^2_1 }$

Answer 1

Answer: (C)

$\frac{FL}{\pi r_1r_2 Y}$

Answer 2

$\Delta L = \frac{FL}{\gamma A} = \frac{FL}{\gamma \sqrt{A_1 A_2}} = \frac{FL}{\gamma \sqrt{\pi r_1^2 r_2^2}}$ $\Delta L = \frac{FL}{\gamma \, \pi \, r_1 r_2}$